Question

Два мебельных мастера, работая вместе,могут за 1 неделю собрать 50 столов. Работая отдельно, первый мастер собирает 60 столов на одну неделю дольше, чем такое же количество столов собирает второй мастер. За сколько недель первый мастер соберет 40 столов?

Answer 1

х-количество столов собирает первый мастер за неделю, у- количество столов собирает второй матсер за неделю

х+у=50

60/х- количество недель для первого матсера собрать 60 столов

60/у -   количество недель для первого матсера собрать 60 столов 

60/х-60/у=1

из первого выражаем х=50-у, подставляем во второе

у² +70у-3000=0

у=30,

х=20 

значит 40/20=2 недели 

Answer 2

1)7-2=5.(дней)мы отнимаем от 7 дней недели 2,так как необходимо узнать,за сколько мастер собирает 40 столов

2)60-40=20(дней)мы отнимаем насколько дольшне получается

3)20:5=4(недели)мы делим дни на дни и получаем недели

Ответ: за 4 недели мастер соберет 40 столов.

Answer 3

Problem Analysis

We are given that two furniture masters can assemble 50 tables in 1 week when working together. However, when working separately, the first master takes one week longer than the second master to assemble the same number of tables. We need to determine how many weeks it will take for the first master to assemble 40 tables.

Solution

Let's assume that the second master can assemble x tables in one week. According to the problem, the first master takes one week longer than the second master to assemble the same number of tables. Therefore, the first master can assemble x tables in x + 1 weeks.

When the two masters work together, they can assemble 50 tables in 1 week. This means that their combined work rate is 50 tables per week. We can set up the following equation to represent their combined work rate:

x + (x + 1) = 50

Simplifying the equation, we get:

2x + 1 = 50

Subtracting 1 from both sides, we have:

2x = 49

Dividing both sides by 2, we find:

x = 24.5

Since we cannot have a fractional number of tables, we can round down to the nearest whole number. Therefore, the second master can assemble 24 tables in one week.

Now, we need to determine how many weeks it will take for the first master to assemble 40 tables. Since the first master takes one week longer than the second master to assemble the same number of tables, the first master will take 25 weeks to assemble 40 tables.

Answer

The first master will take 25 weeks to assemble 40 tables.